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# Solutions for Chapter 9: Factorial Experiments

## Full solutions for Statistics for Engineers and Scientists | 4th Edition

ISBN: 9780073401331

Solutions for Chapter 9: Factorial Experiments

Solutions for Chapter 9
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##### ISBN: 9780073401331

Summary of Chapter 9: Factorial Experiments

In this chapter we will discuss the design of and the analysis of data from a class of experiments known as factorial experiments.

Since 24 problems in chapter 9: Factorial Experiments have been answered, more than 709963 students have viewed full step-by-step solutions from this chapter. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Chapter 9: Factorial Experiments includes 24 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Key Statistics Terms and definitions covered in this textbook
• 2 k p - factorial experiment

A fractional factorial experiment with k factors tested in a 2 ? p fraction with all factors tested at only two levels (settings) each

• All possible (subsets) regressions

A method of variable selection in regression that examines all possible subsets of the candidate regressor variables. Eficient computer algorithms have been developed for implementing all possible regressions

• Analysis of variance (ANOVA)

A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation

• Bernoulli trials

Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

• Bimodal distribution.

A distribution with two modes

• Bivariate distribution

The joint probability distribution of two random variables.

• Bivariate normal distribution

The joint distribution of two normal random variables

• Box plot (or box and whisker plot)

A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

• Components of variance

The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.

• Conditional mean

The mean of the conditional probability distribution of a random variable.

• Contour plot

A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

• Contrast

A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

• Decision interval

A parameter in a tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes.

• Defect

Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.

• Dependent variable

The response variable in regression or a designed experiment.

• Error mean square

The error sum of squares divided by its number of degrees of freedom.

• Error of estimation

The difference between an estimated value and the true value.

• Exhaustive

A property of a collection of events that indicates that their union equals the sample space.

• F-test

Any test of signiicance involving the F distribution. The most common F-tests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

• Fractional factorial experiment

A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.